One meaning of a 'linear' equation is that if you draw the graph of the equation, the graph will be a straight line.
That's an easy way to test the equation . . . find 3 points on the graph, and see whether they're all in a straight line.
This equation is y = 4 / x .
To find a point on the graph, just pick any number for 'x', and figure out the value of 'y' that goes with it. Do that 3 times, and you've got 3 points on the graph.
Here ... I'll do 3 quick points:
Point-A: x = 1 y = 4 / 1 = 4 Point-B: x = 2 y = 4 / 2 = 2 Point-C: x = 4 y = 4 / 4 = 1
Look at this:
Slope of the line from point-A to point-B = (change in 'y') / (change in 'x') = -2 .
Slope of the line from point-B to point-C = (change in 'y') / (change in 'x') = -1/2 .
The two pieces of line from A-B and from B-C don't even have the same slope, so they're not pieces of the same straight line ! So my points A, B, and C are NOT in a straight line.
